Spring Rate Calculator
Enter wire diameter, coil outer diameter and active coils to get the spring rate — the classic k = G·d⁴/(8·D³·n) formula with manufacturability notes.
Last updated: 2026-09-15
How the calculation works
- Torsion of the wire dominates spring deflection; the formula collapses that into one rate expression.
- Wire diameter enters to the 4th power — a 10% thicker wire is 46% stiffer. Coil diameter enters cubed.
- The spring index (D/d) flags manufacturability: below 4 is hard to coil, above 12 is unstable.
Formula
k = G × d⁴ / (8 × D³ × n)
| Symbol | Meaning | Unit |
|---|---|---|
k | Spring rate | N/mm |
G | Shear modulus of the wire | N/mm² |
d | Wire diameter | mm |
D | Mean coil diameter | mm |
n | Active coils | — |
Worked example
4 mm wire, 25 mm OD (21 mm mean), 8 active coils, music wire: k = 79,300 × 256 / (8 × 9,261 × 8) = 34.3 N/mm ≈ 196 lbf/in. Loading it 50 mm takes 1,715 N.
Interpreting the result
Rate is stiffness, not strength — max load depends on stress, which the Wahl correction factor evaluates. The d⁴ sensitivity means wire size is the design lever; coil count fine-tunes. Doubling active coils halves the rate but doubles travel before solid height.
Assumptions
- Round wire, helical compression, linear range.
- Static loading; fatigue needs stress-life analysis.
Limitations
- Wahl stress correction applies at high loads — rate alone doesn't predict failure.
- Conical, barrel and torsion springs don't follow this formula.
Frequently asked questions
How do I make a spring stiffer?
Bigger wire (4th power — very effective), smaller coil diameter (3rd power), or fewer active coils (linear). Grinding ends or adding coils is easier than re-coiling.
What is spring index?
Mean coil diameter ÷ wire diameter. 4–12 manufactures well and performs predictably; outside that range you fight coiling limits or buckling.